From 95c915ce89cc168ec34ab36797c78de94fcc0a18 Mon Sep 17 00:00:00 2001 From: Guillaume Melquiond Date: Wed, 17 Sep 2014 17:45:39 +0200 Subject: Add some missing Proof statements. --- theories/QArith/Qcanon.v | 1 + theories/QArith/Qpower.v | 1 + theories/QArith/Qreals.v | 2 ++ theories/QArith/Qreduction.v | 2 ++ 4 files changed, 6 insertions(+) (limited to 'theories/QArith') diff --git a/theories/QArith/Qcanon.v b/theories/QArith/Qcanon.v index 2ed7a29ea..fb7f4c4a4 100644 --- a/theories/QArith/Qcanon.v +++ b/theories/QArith/Qcanon.v @@ -520,6 +520,7 @@ Add Field Qcfield : Qcft. (** A field tactic for rational numbers *) Example test_field : (forall x y : Qc, y<>0 -> (x/y)*y = x)%Qc. +Proof. intros. field. auto. diff --git a/theories/QArith/Qpower.v b/theories/QArith/Qpower.v index 5d494c7c8..db77567a7 100644 --- a/theories/QArith/Qpower.v +++ b/theories/QArith/Qpower.v @@ -41,6 +41,7 @@ try destruct (Qmult_integral _ _ H0); auto. Qed. Lemma Qpower_pos_positive : forall p n, 0 <= p -> 0 <= Qpower_positive p n. +Proof. intros p n Hp. induction n; simpl; repeat apply Qmult_le_0_compat;assumption. Qed. diff --git a/theories/QArith/Qreals.v b/theories/QArith/Qreals.v index f363fd7c2..8f827dab9 100644 --- a/theories/QArith/Qreals.v +++ b/theories/QArith/Qreals.v @@ -14,6 +14,7 @@ Require Export QArith_base. Definition Q2R (x : Q) : R := (IZR (Qnum x) * / IZR (QDen x))%R. Lemma IZR_nz : forall p : positive, IZR (Zpos p) <> 0%R. +Proof. intros; apply not_O_IZR; auto with qarith. Qed. @@ -162,6 +163,7 @@ field; auto. Qed. Lemma Q2R_minus : forall x y : Q, Q2R (x-y) = (Q2R x - Q2R y)%R. +Proof. unfold Qminus; intros; rewrite Q2R_plus; rewrite Q2R_opp; auto. Qed. diff --git a/theories/QArith/Qreduction.v b/theories/QArith/Qreduction.v index 3b3a30eb9..2aac617eb 100644 --- a/theories/QArith/Qreduction.v +++ b/theories/QArith/Qreduction.v @@ -126,11 +126,13 @@ Proof. Qed. Add Morphism Qmult' : Qmult'_comp. +Proof. intros; unfold Qmult'. rewrite H, H0; auto with qarith. Qed. Add Morphism Qminus' : Qminus'_comp. +Proof. intros; unfold Qminus'. rewrite H, H0; auto with qarith. Qed. -- cgit v1.2.3